Finite Group Databasebeta

← #11747749

Subgroups — #11747749

Order 960.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#677C211yesmaximal, characteristic
2#91434C211yesmaximal, characteristic
3#91385C211yesmaximal, characteristic, complemented
4C2×#6655C211yesmaximal, characteristic
5#91098C211yesmaximal, characteristic, complemented
6C5×#816C211yesmaximal, characteristic, complemented
7#90970C211yesmaximal, characteristic, complemented
8#65107—31nomaximal, Hall
9C2×C5×Dic6C2211yescharacteristic
10C2×C3×D20C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C2×D5×Dic3—21no—
13C2×C3×C5×C8C2211yescharacteristic
14C4×Dic15C2211yescharacteristic
15C2×C3⋊#168C2211yescharacteristic
16C5×C4⋊Dic3C2211yescharacteristic
17C3×#677—22no—
18#6669—21no—
19#6669—21no—
20#6665—21no—
21#6655—22no—
22#5162—51nomaximal, Hall
23#4090—31no—
24C2×#688—31no—
25C2×#677D311yescharacteristic
26#4039—31no—
27C5×#103—31no—
28#3946—31no—
29#3942—31no—
30C22×C3×D5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15D411yescharacteristic
33C2×Dic15D411yescharacteristic
34C2×C5×Dic3—21no—
35C2×C5×Dic3—21no—
36C5×Dic6—21no—
37C5×Dic6—21no—
38C2×C3×Dic5—21no—
39C3×D20—21no—
40C3×D20D412yes—
41C3×Dic10—21no—
42C3×Dic10—21no—
43D5×Dic3—42no—
44C3×C5×C8—21no—
45C3⋊#168—21no—
46C2×C3×SD16—51no—
47#944—51no—
48D4×Dic3—51no—
49C2×#214—51no—
50#835—51no—
51#816D511yescharacteristic, complemented
52Dic3⋊C8—51no—
53C2×C5×Q8—31no—
54C2×D20C2×D311yescharacteristic
55C2×C4×D5—61no—
56C2×Dic10C2×D311yescharacteristic
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4—31no—
59#688—62no—
60#685—61no—
61#683—61no—
62#683—61no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—22no—
66#461—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C3×D5—22no—
69C2×C3×D5—41no—
70C2×C3×D5—41no—
71C3×C4×C5C2×D411yescharacteristic
72C3×C4×C5#4111yescharacteristic
73Dic15—21no—
74Dic15SD1612yescomplemented
75C3×Dic5—41no—
76C5×Dic3—41no—
77C5×Dic3—41no—
78C2×C3×Q8—51no—
79C2×C3×D4—51no—
80C22×Dic3—101no—
81C2×Dic6C2×D511yescharacteristic
82C3×SD16—102no—
83C2×C3×C8C2×D511yescharacteristic
84#217—101no—
85#214—102no—
86C4⋊Dic3C2×D511yescharacteristic
87Dic3⋊C4—101no—
88Dic3⋊C4—101no—
89C4×Dic3—51no—
90C2×C3⋊C8—51no—
91C22×D5—21no—
92C5×Q8—61no—
93C5×Q8—61no—
94C2×C4×C5—61no—
95C2×C4×C5—61no—
96C2×C4×C5C22×D311yescharacteristic
97C2×Dic5—21no—
98C2×Dic5—31no—
99C2×Dic5—31no—
100D20—21no—
101D20#6712yes—
102C4×D5—122no—
103Dic10—21no—
104Dic10—21no—
105C5×C8—21no—
106#168—61no—
107C2×SD16—51no—
108C2×SD16—151no—
109C4⋊Q8—151no—
110C4×D4—151no—
111C4⋊C8—151no—
112#103—31no—
113#103—151no—
114C2×C3×C5#12111yescharacteristic
115C2×C3×C5C2×SD1611yescharacteristic
116C2×C3×C5#13711yescharacteristic
117C3×D5—42no—
118C23×C3—101no—
119C3×Q8—101no—
120C3×Q8—101no—
121C3×D4—52no—
122C3×D4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22×D511yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—21no—
127C2×Dic3—51no—
128C2×Dic3—51no—
129C2×Dic3—202no—
130Dic6—21no—
131Dic6—21no—
132C3×C8—21no—
133C3⋊C8—101no—
134C22×C5D3×D411yescharacteristic
135C2×D5—22no—
136C2×D5—41no—
137C2×D5—41no—
138C4×C5—121no—
139C4×C5—121no—
140C4×C5#23711yescharacteristic
141C4×C5C2×#6711yescharacteristic
142Dic5—32no—
143Dic5—41no—
144Dic5—61no—
145C2×Q8—31no—
146C2×Q8—51no—
147C2×D4—51no—
148C22×C4—301no—
149SD16—102no—
150SD16—302no—
151C2×C8—151no—
152C2×C8D3×D511yescharacteristic
153C4⋊C4—31no—
154C4⋊C4—301no—
155C4⋊C4—301no—
156C22⋊C4—301no—
157C42—151no—
158C3×C5#46111yescharacteristic, complemented, Hall
159C22×C3—102no—
160C22×C3—201no—
161C22×C3—201no—
162C22×C3D4×D511yescharacteristic
163C3×C4—201no—
164C3×C4#70911yescharacteristic
165C3×C4D4×D511yescharacteristic
166Dic3—41no—
167Dic3—41no—
168Dic3—52no—
169Dic3—101no—
170C2×C5D3×SD1611yescharacteristic
171C2×C5#91511yescharacteristic
172C2×C5#93911yescharacteristic
173D5—42no—
174C23—101no—
175Q8—61no—
176Q8—61no—
177Q8—101no—
178Q8—101no—
179D4—52no—
180D4—101no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—101no—
184C2×C4—151no—
185C2×C4—151no—
186C2×C4—602no—
187C2×C4C2×D3×D511yescharacteristic
188C8—21no—
189C8—301no—
190C2×C3—202no—
191C2×C3#403011yescharacteristic
192C2×C3D5×SD1611yescharacteristic
193C2×C3#406411yescharacteristic
194C5#516211yescharacteristic, complemented, Sylow
195C22—102no—
196C22—201no—
197C22—201no—
198C22#677711yescharacteristic
199C4—121no—
200C4—121no—
201C4—152no—
202C4—201no—
203C4—301no—
204C4#676511yescharacteristic
205C4D5×#6711yescharacteristic
206C3#6510711yescharacteristic, complemented, Sylow
207C2—202no—
208C2#9125511yescharacteristic
209C2#9127811yescharacteristic
210C2#9140811yescharacteristic
subgroupG/H
centerC22#6777
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D20C22
hypercenterC2×C8D3×D5
hypocenterC3×C5#461
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #91385C2semidirect
5. #91098C2semidirect
6. C5×#816C2semidirect
7. #90970C2semidirect
51. #816D5semidirect
74. Dic15SD16semidirect
158. C3×C5#461semidirect
194. C5#5162semidirect
206. C3#65107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#6772
#914342
#913852
C2×#66552
#910982
C5×#8162
#909702
#651073
#51625